Hello guys. I want to share something with you today. A mathematical magic if you will. It is called the Hooper's Paradox ,you can find more here (nolinks://nolinks.cut-the-knot.org/Curriculum/Fallacies/HooperParadox.shtml) or searching google. nolinks://nolinks.cut-the-knot.org/Curriculum/Fallacies/HooperParadox.shtml (nolinks://nolinks.cut-the-knot.org/Curriculum/Fallacies/HooperParadox.shtml) I suggest you go and read the article. What it says basically is that : you can take a geometrical shape,rearrange it and change it`s area! I can`t even believe this is possible! I`m speechless! What do you guys think?
I have a headake! ;)
cut 3 chips and you will have 3.2 chips? LOL
I am not smart enough
A = 3 m x 4 m = 12 square metres.
A = 1 m x 12 m = 12 square metres
A = 2 m x 6 m = 12 square metres
so the perimeter of A = 14m
the perimeter of B = 26m
the perimeter of C = 16m
So just by looking at that, the reverse should be easily achieved. I hope i understand the problem correctly. lolol
Cheers
Jakk
Jakk, any chance you can apply that mind to the table??? ;D
It doesn't work. The area doesn't really increase, it only appears to increase because the pieces are poorly assembled.
Here's my response to the bogus shapes. I'm not sure that all my math terms are written properly, but certainly the essence is accurate, unlike the paradox site. A paradox seems untrue, this in fact IS untrue. Note the word 'fallacies' in the long title of the link to the site.
the angle created by splitting the rectangle in half is which forms the large triangles is (3/10=.3)
3/10 tangent = 16.69924423 degree angle
16.69924423 cotangent = 3.33333333333
opposite side right triangle * cotangent angle = adjacent side
2 (as it is drawn) * 3.33333333 = 6.66666666 = 6 2/3 not 6 as it is drawn
the area of the two triangles together as would be 2 * 6 2/3 = 13 1/3 not 12 as it is drawn/written
the two trapezoids would be 3 1/3 * 5 = 16 2/3
16 2/3 + 13 1/3 = 30
the area of the newly configured shapes are also 30
the sum of the parts equals the whole (area anyway, not necessarily perimeter)
Ever heard of Hooper's paradox??????????????????? Hooper's horse shit perhaps????????????
RP
The line going thru the rectangle in the second pic is not a straight line ie the angle of the line is changed.
It is sleight of hand. There should not be any change in the total area of the shapes.
As for the HG, I do want some of that cake if any of you have it.
Someone with some geometry take a look at this. I saw it in a magazine of puzzles.
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A piece of string stretched around the board can be re-arranged to create a square with five times the area of the rectangle. However the original board can never be cut in such a way to create more than 18 sq ft. How can the string which describes the first rectangle create an area greater than the original?
You can take this to the extremes by using 1 inch by 18 ft 11 inches and you get virtually no area for your string. A string in a circle will contain the most area. In Oklahoma we have a round barn built for this reason.
Sam
That's where they put the crop circles. >:D
pretend you have 18 pennies, whether they are in a line of pennies or in a 3 by 6 square of pennies you still have 18 pennies, no extra pennies appear or anything do they
Ryan
Nope, No more pennies and no more board.
But if you carefully stretched a string around the outer edges of those pennies and then fashioned it into a square, your original 18 pennies would fit into the square with room to spare.
So if you had a limited amount of material and wanted to build the biggest house possible, you would build a square or circular house, not an oblong one.
Some people find this fact a curiosity and some don't.
Sam
the area doesnt change no matter what you do, thats my point
hoper35
I don't think we've ever had a crop circle in Oklahoma. Or a crop square or triangle. I think the English mostly get those. Been around for hundreds of years, or so I heard.
Sam
How about a place to hold a round-up then?
Ron.